MONTE CARLO APPROACH ON DOUBLE-LAYER MAGNETIC SPIN LATTICE IN ANISOTROPIC HEISENBERG MODEL

2009 ◽  
Vol 23 (02) ◽  
pp. 251-264
Author(s):  
EUGEN BÎRSAN ◽  
OLIVIAN NIGA
Keyword(s):  
Monte Carlo ◽  
Double Layer ◽  
Heisenberg Model ◽  
Finite Size ◽  
Finite Size Effect ◽  
Parameter Distribution ◽  
Physical Parameters ◽  
Model Parameters ◽  
Critical Temperatures ◽  
Anisotropic Heisenberg Model

In this paper, we investigate the magnetic properties of double-layer thin film using Monte Carlo technique, in anisotropic Heisenberg model. The magnetization, out-of-plane and in-plane magnetic susceptibilities, and also the specific heat behaviors according to temperature are investigated in order to find out the contingent magnetic ordering phases and the critical temperatures values, for two easy-axis anisotropy parameters settings. We also calculate the relative variation rate of the critical temperature along with the easy-plane anisotropy interaction parameter distribution, and we comparatively appraise the numerical obtained results, in order to get quantitative response on the physical model parameters changes. Finally, we present a finite size effect study on magnetic susceptibility, respecting the two settings physical parameters we assumed in the paper.

A theoretical consideration of ion size effects on the electric double layer and voltammetry of nanometer-sized disk electrodes

2016 ◽  
Vol 193 ◽  
pp. 251-263 ◽  
Author(s):  
Yu Gao ◽  
Yuwen Liu ◽  
Shengli Chen
Keyword(s):  
Size Effect ◽  
Double Layer ◽  
Electric Double Layer ◽  
Finite Size ◽  
Finite Size Effect ◽  
The Poisson Equation ◽  
Electrochemical Interface ◽  
Disk Electrodes ◽  
Ion Size ◽  
Electrochemical Interfaces

Considering that an electric-double-layer (EDL) structure may significantly impact on the mass transport and charge transfer kinetics at the interfaces of nanometer-sized electrodes, while EDL structures could be altered by the finite sizes of electrolyte and redox ions, the possible effects of ion sizes on EDL structures and voltammetric responses of nanometer-sized disk (nanodisk) electrodes are investigated. Modified Boltzmann and Nernst–Planck (NP) equations, which include the influence of the finite ion volumes, are combined with the Poisson equation and modified Butler–Volmer equation to gain knowledge on how the finite sizes of ions and the nanometer sizes of electrodes may couple with each other to affect the structures and reactivities of a nanoscale electrochemical interface. Two typical ion radii, 0.38 nm and 0.68 nm, which could represent the sizes of the commonly used aqueous electrolyte ions (e.g., the solvated K+) and the organic electrolyte ions (e.g., the solvated TEA+) respectively, are considered. The finite size of ions can result in decreased screening of electrode charges, therefore magnifying EDL effects on the ion transport and the electron transfer at electrochemical interfaces. This finite size effect of ions becomes more pronounced for larger ions and at smaller electrodes as the electrode radii is larger than 10 nm. For electrodes with radii smaller than 10 nm, however, the ion size effect may be less pronounced with decreasing the electrode size. This can be explained in terms of the increased edge effect of disk electrodes at nanometer scales, which could relax the ion crowding at/near the outer Helmholtz plane. The conditions and situations under which the ion sizes may have a significant effect on the voltammetry of electrodes are discussed.

HIGH-PRECISION MONTE CARLO DETERMINATION OF α/ν IN THE 3D CLASSICAL HEISENBERG MODEL

1994 ◽  
Vol 05 (02) ◽  
pp. 267-270
Author(s):  
CHRISTIAN HOLM ◽  
WOLFHARD JANKE
Keyword(s):  
Monte Carlo ◽  
Specific Heat ◽  
Heisenberg Model ◽  
Three Dimensional ◽  
Finite Size ◽  
Topological Defects ◽  
Accurate Estimate ◽  
Scaling Analysis ◽  
Classical Heisenberg Model ◽  
Cluster Monte Carlo

To study the role of topological defects in the three-dimensional classical Heisenberg model we have simulated this model on simple cubic lattices of size up to 803, using the single-cluster Monte Carlo update. Analysing the specific-heat data of these simulations, we obtain a very accurate estimate for the ratio of the specific-heat exponent with the correlation-length exponent, α/ν, from a usual finite-size scaling analysis at the critical coupling Kc. Moreover, by fitting the energy at Kc, we reduce the error estimates by another factor of two, and get a value of α/ν, which is comparable in accuracy to best field theoretic estimates.

Finite-size scaling in ferromagnetic spin systems on the pyrochlore lattice

2020 ◽  
pp. 255-266
Author(s):  
K.S. Soldatov ◽  
◽  
M.A. Padalko ◽  
V.S. Strongin ◽  
D.Yu. Kapitan ◽  
...  
Keyword(s):  
Heisenberg Model ◽  
High Performance ◽  
Finite Size ◽  
Spin Systems ◽  
Xy Model ◽  
Finite Size Scaling ◽  
Critical Temperatures ◽  
Cluster Algorithms ◽  
Size Scaling ◽  
Classical Heisenberg Model

In this paper we present the results of the high-performance computations for the Ising model, the XY-model and the classical Heisenberg model for the pyrochlore lattice. We used Wolff and Swendsen-Wang cluster algorithms with GPU parallelization for the calculations. We obtained critical exponents and critical temperatures using finite-size scaling approach.

THE RESTRICTED SPIN MODEL

1990 ◽  
Vol 04 (16) ◽  
pp. 1029-1041
Author(s):  
H.A. FARACH ◽  
R.J. CRESWICK ◽  
C.P. POOLE
Keyword(s):  
Monte Carlo ◽  
Critical Temperature ◽  
Heisenberg Model ◽  
Anisotropy Parameter ◽  
Finite Size ◽  
Universality Class ◽  
Spin Model ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Monte Carlo Calculations

We present a novel anisotropic Heisenberg model in which the classical spin is restricted to a region of the unit sphere which depends on the value of the anisotropy parameter Δ. In the limit Δ→1, we recover the Ising model, and in the limit Δ→0, the isotopic Heisenberg model. Monte Carlo calculations are used to compare the critical temperature as a function of the anisotropy parameter for the restricted and unrestricted models, and finite-size scaling analysis leads to the conclusion that for all Δ>0 the model belongs to the Ising universality class. For small A the critical behavior is clearly seen in histograms of the transverse and longitudinal (z) components of the magnetization.

scholarly journals UNIVERSAL FINITE-SIZE-SCALING FUNCTIONS

1996 ◽  
Vol 07 (03) ◽  
pp. 287-294 ◽  
Author(s):  
YUTAKA OKABE ◽  
MACOTO KIKUCHI
Keyword(s):  
Monte Carlo ◽  
Distribution Function ◽  
Order Parameter ◽  
Finite Size ◽  
Square Lattice ◽  
Parameter Distribution ◽  
Scaling Functions ◽  
Finite Size Scaling ◽  
Size Scaling ◽  
Regular Lattices

The idea of universal finite-size-scaling functions of the Ising model is tested by Monte Carlo simulations for various lattices. Not only regular lattices such as the square lattice but quasiperiodic lattices such as the Penrose lattice are treated. We show that the finite-size-scaling functions of the order parameter for various lattices are collapsed on a single curve by choosing two nonuniversal scaling metric factors. We extend the idea of the universal finite-size-scaling functions to the order-parameter distribution function. We pay attention to the effects of boundary conditions.

MONTE CARLO STUDY OF MULTILAYER FILMS USING ANISOTROPIC EXTENDED HEISENBERG MODEL WITH DIPOLAR INTERACTION

2009 ◽  
Vol 23 (04) ◽  
pp. 643-653 ◽  
Author(s):  
E. BÎRSAN ◽  
A. DOBRITA ◽  
R. CHIS
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Basal Layer ◽  
Magnetic Ordering ◽  
Monte Carlo Study ◽  
Magnetic Phase Transitions ◽  
Physical Parameters ◽  
Critical Temperatures ◽  
Two Phase ◽  
Antiferromagnetic Ordering

Using the Monte Carlo technique, we study the multilayer Heisenberg thin film with long range dipolar interactions, in order to investigate the antiferromagnetic basal layer influence on the superior layers. We find out that the basal layer's influence over the magnetic ordering of the superior layers is dependent on the distance between that layer and the basal layer, and the exchange anisotropy discontinuity has a direct effect on the critical temperatures associated with the magnetic phase transitions that can occur for different settings of the investigated system physical parameters. In the intermediate dipolar parameter region, due to antiferromagnetic ordering of the basal layer spins, we found out the mixed phase appearance in the superior layers and we relieved two phase transitions which can take place in the system, the critical temperature we obtained by studying the specific heat and the magnetic susceptibility, respectively, being in good agreement.

Monte Carlo Simulations of Growth Kinetics and Phase Transitions at Interfaces: Some Recent Results

1991 ◽  
Vol 237 ◽  
Author(s):  
P. Nielaba ◽  
K. Binder
Keyword(s):  
Monte Carlo ◽  
Phase Transitions ◽  
Fluid Layer ◽  
Finite Size ◽  
Critical Temperatures ◽  
Infinite Layer ◽  
Limit Value ◽  
Monte Carlo Studies ◽  
Coexistence Densities ◽  
Kinetics Of

ABSTRACTIn the first part Monte Carlo studies of the kinetics of multilayer adsorption (without screening) are described. The approach to the jamming coverage in each layer is asymptotically exponential. The jamming coverages approach the infinite-layer limit value according to a power law. In the second part, studies of phase transitions in two dimensional fluids are reviewed. With a combination of Monte Carlo and finite size scaling block analysis techniques, accurate values are obtained for the critical temperatures, coexistence densities and the compressibilities of an adsorbed fluid layer in an NVT ensemble.

Sensitivity analysis of an urban stormwater microorganism model

2010 ◽  
Vol 62 (6) ◽  
pp. 1393-1400 ◽  
Author(s):  
D. T. McCarthy ◽  
A. Deletic ◽  
V. G. Mitchell ◽  
C. Diaper
Keyword(s):  
Sensitivity Analysis ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Analysis ◽  
Parameter Distribution ◽  
Model Parameters ◽  
Urban Stormwater ◽  
Urban Catchments ◽  
Two Parameters

This paper presents the sensitivity analysis of a newly developed model which predicts microorganism concentrations in urban stormwater (MOPUS—MicroOrganism Prediction in Urban Stormwater). The analysis used Escherichia coli data collected from four urban catchments in Melbourne, Australia. The MICA program (Model Independent Markov Chain Monte Carlo Analysis), used to conduct this analysis, applies a carefully constructed Markov Chain Monte Carlo procedure, based on the Metropolis-Hastings algorithm, to explore the model's posterior parameter distribution. It was determined that the majority of parameters in the MOPUS model were well defined, with the data from the MCMC procedure indicating that the parameters were largely independent. However, a sporadic correlation found between two parameters indicates that some improvements may be possible in the MOPUS model. This paper identifies the parameters which are the most important during model calibration; it was shown, for example, that parameters associated with the deposition of microorganisms in the catchment were more influential than those related to microorganism survival processes. These findings will help users calibrate the MOPUS model, and will help the model developer to improve the model, with efforts currently being made to reduce the number of model parameters, whilst also reducing the slight interaction identified.

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